Measuring Intertemporal Substitution:

The Importance of Method Choices and Selective Reporting∗

Tomas Havranek

Czech National Bank and Charles University, Prague

tomas.havranek@ies-prague.org

September 15, 2014

Abstract

I examine 2,735 estimates of the elasticity of intertemporal substitution in consumption

(EIS) reported in 169 published studies. The literature shows strong selective reporting:

researchers discard negative and insignificant estimates too often, which pulls the mean

estimate up by about 0.5. The reporting bias dwarfs the effects of methods, with the

exception of the choice between micro and macro data. When I correct the mean for the

bias, for macro estimates I get zero, even though the reported t-statistics are on average

two. The corrected mean of micro estimates of the EIS for asset holders is around 0.3–0.4.

Calibrations greater than 0.8 are inconsistent with the bulk of the empirical evidence.

Keywords: Elasticity of intertemporal substitution, consumption, publication

bias, meta-analysis

JEL Codes: E21, C83

1 Introduction

The elasticity of intertemporal substitution in consumption, a key input into macroeconomic

models, has been estimated by hundreds of researchers. Their estimates vary greatly, and it is

unclear what values should be used for calibration. One of the first surveys on the micro evidence

from consumption Euler equations, Browning & Lusardi (1996), puts it in the following way:

∗An online appendix with data, code, and additional results is available at meta-analysis.cz/eis.

1

It is frustrating in the extreme that we have very little idea of what gives rise to the

different findings. (. . . ) We still await a study which traces all of the sources of dif-

ferences in conclusions to sample period; sample selection; functional form; variable

definition; demographic controls; econometric technique; stochastic specification;

instrument definition; etc. (p. 1833)

I explore whether the variation in the estimates of the EIS can be attributed to method choices

and selective reporting. My results suggest that the findings of the literature are, on average,

biased upwards because of the tendency of some authors to preferentially report positive and

statistically significant estimates. The bias stemming from selective reporting is stronger than

the biases associated with the supposed misspecifications in the measurement of the elasticity.

The first issue I focus on, selective reporting, reflects researchers’ priors concerning the

correct value of the parameter and, in many cases, can be beneficial at the level of individual

studies. Suppose, for example, that a researcher estimates a negative elasticity of intertemporal

substitution. A negative EIS implies convex utility, so the estimate is probably a statistical

artifact. One should get negative estimates from time to time when the underlying EIS is small

or estimation is imprecise, yet it makes little sense to build conclusions on them. The problem

is that no upper limit exists which would mirror the lower limit of zero given by the theory:

if many researchers discard negative estimates but most report large positive ones, our inference

from the literature as a whole gets biased.

The second issue I explore is the influence of method choices on results. To this end, for each

estimate of the EIS I collect information on the definition of the utility function used by the

authors, characteristics of the data, definition of variables, inclusion of controls, and estimation

technique, and regress the reported elasticities on these characteristics of methodology. I also

control for differences in publication characteristics, such as the number of citations and the

journal impact factor. Then I compare the extent of the bias stemming from various supposed

misspecifications in the measurement of the EIS discussed in the literature with the extent of

the bias attributable to selective reporting.

To measure the selective reporting bias I exploit the property of most techniques used by

researchers to estimate the EIS: the ratio of the point estimate to its standard error has a

t-distribution. This property implies that the reported estimates should not be correlated with

2

their standard errors. But when I regress the estimates on their standard errors I get a coefficient

of about two—even if I control for 30 variables reflecting the context in which researchers obtain

the estimates. The finding indicates that the reported t-statistic tends to equal two no matter

how large the underlying elasticity is, reflecting the authors’ preference to report positive and

statistically significant estimates. The constant in this regression is zero, which suggests that

the mean underlying elasticity beyond the bias is negligible. Therefore, the mean EIS reported

in the literature, 0.5, equals the selective reporting bias.

The reporting bias seems to dwarf the effects of the supposed misspecifications, with the

exception of the choice between micro and macro data and between asset holders and all con-

sumers. The micro studies report a positive elasticity even after correction for selective re-

porting: on average about 0.2. The corrected mean estimate reaches 0.3–0.4 for estimates

associated with asset holders, which I consider the literature’s best shot for the calibration of

the EIS. Vissing-Jorgensen (2002) argues that including non-asset holders creates a downward

bias in the estimated elasticity, because the corresponding Euler equation is not valid for house-

holds that do not participate in asset markets. My results suggest that the empirical literature

on the EIS does not support calibrations greater than 0.8, the largest upper bound I get for the

asset holders’ elasticity.

2 Data

I search in Google Scholar for studies that estimate the EIS using consumption Euler equations.

My search query is available in the online appendix along with all data and the list of studies

examined after the search. A total of 169 published papers report an estimate of the EIS and

its standard error or a statistic from which the standard error can be computed. I collect all

estimates from the papers and also codify 30 variables reflecting the context in which researchers

obtain the elasticities (Table A2 in the Appendix). I add the last study to the data set on

January 1, 2013, and terminate the search. The oldest study was published in 1981, and the

ten most recent ones in 2012. The 169 studies combined provide 2,735 estimates, which makes

this paper, to my knowledge, the largest meta-analysis conducted in economics. Doucouliagos

& Stanley (2013) survey 87 economic meta-analyses and report that the largest one includes

1,460 estimates from 124 studies.

3

Many unpublished papers provide estimates of the EIS as well, but I focus on published

studies. I have three reasons for this restriction. First, publication status is a simple indicator

of quality. Second, it would take many months to collect all information from the unpublished

studies. Third, there is evidence for little differences in the extent of selective reporting between

published and unpublished studies in economics (for example, Rusnak et al., 2013). Neverthe-

less, as a robustness check, in the next section I also include a small sample of unpublished

studies. I additionally collect estimates of the coefficient of relative risk aversion if the coeffi-

cient also determines the EIS—if researchers assume time-separable utility, the same parameter

determines both risk aversion and the inverse of the EIS. In this case I approximate the standard

error of the EIS by the delta method.

The mean reported estimate from all studies is 0.5. For the computation I exclude estimates

that are larger than 10 in absolute value because they would influence the unweighted average

heavily. (Later in the analysis I use precision as the weight, and these large estimates are usually

imprecise, so I leave them in the data set.) The mean estimate reported in the literature thus

corresponds to the common calibration value referred to, for example, by Trabandt & Uhlig

(2011), Jeanne & Ranciere (2011), Jin (2012), and Rudebusch & Swanson (2012).1 But the

arithmetic mean is driven by studies reporting many estimates. As a next step I select the

median estimate from each study: the mean of medians is even larger than the mean of all

estimates and reaches 0.7. For micro studies (42 out of the 169 studies in the data set) I get a

mean EIS of 0.8. The data set also includes 33 studies published in the top five general interest

journals; these studies report the EIS to be 0.9 on average.

If I stopped here I would argue that the empirical evidence of the last three decades, when

more weight is given to micro studies and the best journals, is consistent with calibration of the

EIS close to one. Logarithmic utility would seem to be a good approximation of the isoelastic

utility function. This conclusion could be a mistake, though, since not all estimates have the

same probability of being reported. If researchers intentionally or unintentionally suppress

negative or insignificant estimates, the mean reported elasticity gets biased upwards.

1Table A1 in the Appendix illustrates, however, that calibrations of the EIS routinely differ by an order ofmagnitude.

4

3 Selective Reporting

The workhorse tool for the estimation of the EIS is the log-linearized consumption Euler equa-

tion. Researchers typically follow Hall (1988) and estimate

∆ct+1 = α+ EIS0 · rt+1 + εt+1, (1)

where ∆ct+1 stands for consumption growth at time t + 1, rt+1 is the real return on an asset

at time t + 1 (for example the treasury bill return or stock market return), and εt+1 is the

error term. Because the error term is correlated with rt+1, researchers use instruments for

rt+1, usually including the rate of return and consumption growth known at time t. (The

many modifications and alternatives to (1) are discussed and controlled for in the next section.)

If EIS0 is the same across all studies, estimates of EIS0, typically obtained using two-stage

least squares (TSLS) or the general method of moments (GMM), will be t-distributed. More

importantly, the ratio of the estimate of EIS0 to its standard error has a t-distribution.

The t-distribution of the ratio implies that the numerator (the point estimate of the EIS)

should be independent of the denominator (the standard error of the estimate). In the absence of

selective reporting the reported estimates are therefore uncorrelated with their standard errors

(Card & Krueger, 1995):

EISij = EIS0 + β · SE(EISij) + uij , (2)

where EISij and SE(EISij) are the i-th estimates of the elasticity of intertemporal substitution

and their standard errors reported in the j-th studies; uij is a disturbance term reflecting

sampling error. The coefficient β should be zero if all estimates have the same probability of

being reported.

Researchers in medicine, among others, have long been concerned with selective reporting.

The best medical journals now require registration of clinical trials before publication of results

(Stanley, 2005). Similarly the American Economic Association has agreed to establish a registry

for randomized control trials “to counter publication bias” (Siegfried, 2012, p. 648), with the

eventual intention to make registration necessary for submission to the Association’s journals.2

It appears infeasible to impose this requirement in other fields of empirical economics, although

2I use “selective reporting bias,” which I believe is more appropriate than the common term “publication

5

there is little reason to believe they are free of the bias. Selective reporting in various fields has

been mentioned by, for example, DeLong & Lang (1992), Card & Krueger (1995), Stanley (2001),

Gorg & Strobl (2001), and Ashenfelter & Greenstone (2004). When registries of empirical

research are missing, meta-analysis represents the only way to correct for the bias.

Selective reporting has two potential sources. First, researchers may discard negative esti-

mates, which are inconsistent with the theory since they imply a convex utility function. In

this case I would obtain a positive estimate of β because of the heteroskedasticity of (2): With

low standard errors the estimates lie close to the mean underlying elasticity. As the standard

errors increase, the estimates get more dispersed, and some get large. If researchers discard the

negative estimates but keep the large positive ones, a positive correlation between EISij and

SE(EISij) arises. Second, researchers (or editors or referees) may prefer statistically significant

estimates. In that case researchers need large estimates of the EIS to offset the standard errors,

and again I obtain a positive estimate of β. If the underlying elasticity is zero but researchers

desire a positive estimate significant at the 5% level, they need t-statistics of about two, so the

estimated β will be close to two.

The constant in regression (2), EIS0, denotes the underlying elasticity corrected for selec-

tive reporting: the mean EIS conditional on standard errors approaching zero. The constant

(corrected EIS) can also be computed approximately as the mean uncorrected EIS less the mean

extent of publication bias, β ·SE(EIS). I have noted that (2) is heteroskedastic, and the degree

of heteroskedasticity is determined by the estimates’ standard errors. To achieve efficiency I

use weighted least squares with the inverse of the standard error, the estimates’ precision, as

the weight (Stanley, 2008). In all regressions that include multiple estimates from one study I

cluster standard errors at the study level. I prefer to estimate the equation with study fixed

effects to remove the influence of the studies’ characteristics.

The first column of Table 1 reports the baseline result. The estimated β is approximately two

and the constant equals zero, suggesting strong selective reporting and zero underlying elasticity

on average. Because 80% of the reported estimates are positive, as much as 1,641 (60% of 2,735)

negative estimates may be missing in the literature because of selective reporting. This result

suggests that researchers report only a quarter of all negative estimates. Moreover, half of the

bias” used in medical science and many applications of meta-analysis in social sciences. The bias can be presentin all reported manuscripts, published or unpublished.

6

positive estimates have a t-statistic above two, which would indicate that researchers discard

90% of estimates if we accepted that the underlying elasticity was zero for all studies.

Table 1: The reported estimates are correlated with their standard errors

FE BE Median Micro Top Country

SE 2.115∗∗∗

3.020∗∗∗

2.719∗∗∗

1.496∗∗

1.466∗

2.117∗∗∗

(0.205) (0.573) (0.397) (0.717) (0.825) (0.216)

Constant 0.0145 0.0303∗∗∗

0.0322∗∗∗

0.174∗∗∗

0.171∗

0.0144(0.00881) (0.00656) (0.00893) (0.0554) (0.0887) (0.00928)

Observations 2,735 2,735 2,735 512 566 2,735Studies 169 169 169 42 33 169

Notes: The table presents the results of regression EISij = EIS0+β ·SE(EISij)+uij . EISij and SE(EISij)are the i-th estimates of the elasticity of intertemporal substitution and their standard errors reported in thej-th studies. Estimated by weighted least squares with the inverse of the reported estimate’s standard errortaken as the weight. Standard errors of regression parameters are robust, clustered at the study level, andshown in parentheses. FE = study fixed effects. BE = between effects. Median = only median estimates ofthe EIS reported in the studies are included. Micro = only micro estimates of the EIS are included. Top =only estimates of the EIS from the top 5 journals are included. Country = country and study fixed effects.∗∗∗

,∗∗

, and∗

denote statistical significance at the 1%, 5%, and 10% level.

In the second and third column of the table I use the average and median values reported

in the studies. The evidence for selective reporting gets stronger when between-study instead

of within-study variation is used. The estimated magnitude of the bias increases to 2.7–3, and

both regressions identify a significant but small underlying EIS of about 0.03. The bias seems to

be smaller in micro studies and studies published in the top five journals, but not by much—by

approximately 25% compared to all studies. Moreover, micro studies and studies published

in top journals show a positive EIS, about 0.2, even after correction for selective reporting.

Because it is easier for micro studies to identify a positive EIS, researchers do not have to

search long for an intuitive result, which leads to less selective reporting. Studies published in

top journals use micro data more often than other studies, which also leads to a smaller bias.

In the last column of the table I add country fixed effects to the baseline specification, because

the estimates cover 120 different countries (although more than half of all the estimates use

data on the US).3 The result is similar to the case when I employ only study fixed effects: the

magnitude of the reporting bias is large and the mean EIS corrected for the bias is negligible.

To compare the extent of selective reporting between published and unpublished studies,

I collect data from 50 working papers. I use the same search strategy as for the published

3In Havranek et al. (2013) we examine the cross-country heterogeneity in the estimates of the EIS.

7

studies, but only include working papers whose latest version was detected by Google Scholar

in 2007 or earlier; that is, at least five years prior to the end of my search period for published

studies. I exclude newer working papers because, due to publication lags in economics, many

of them may still be published. The results are provided in the online appendix. Unpublished

studies show less selective reporting, but the difference is statistically insignificant. Overall,

my results suggest that selective reporting arises primarily from the researchers’ priors about

what constitutes a plausible and interesting result, not from the preferences of editors and

referees—although the priors may be formed based on what results are publishable.

The online appendix shows four additional robustness checks. First, I test whether my

results change if I only consider estimates of the EIS published in finance journals. Different

values of the elasticity are needed to explain different facts in economics and finance; perhaps

the two streams of literature differ in the extent of selective reporting. Nevertheless, my results

suggest that the estimates of the EIS reported in finance are very similar to those reported in

economics. Second, some studies report asymmetric confidence intervals for the estimates, which

means that the ratio of the point estimate to the standard error is not t-distributed. I follow

the advice of Stanley (2001, p. 135) to “better err on the side of inclusion” in meta-analysis,

compute approximate standard errors for the estimates (based on the simplifying assumption of

normal distribution), and include the estimates. Exclusion of these estimates does not change

my results. Third, I exclude the three studies from my sample that use the long-run risks

model to estimate the EIS, but the results are again similar. Finally, my results do not change

qualitatively if I exclude estimates with bootstrapped confidence intervals.

It is difficult to say at this point which of the two potential sources of selective reporting

drives the results in Table 1. A graphical inspection of the data suggests that both sources play

a role. Figure 1 shows the so-called funnel plot, which is often used in medical meta-analyses to

detect selective reporting (Egger et al., 1997). The horizontal axis measures the magnitude of

the estimate of the EIS, while the vertical axis measures the estimate’s precision, the inverse of

the standard error. The most precise estimates should be concentrated close to the underlying

effect at the top of the figure, while the imprecise estimates at the bottom should be more

dispersed. The t-distribution of the ratio of point estimates to their standard errors ensures

that in the absence of selective reporting the figure is symmetrical, forming an inverted funnel.

8

Figure 1: Negative estimates are underreported

(a) All estimates

05

1015

2025

prec

isio

n of

the

estim

ate

(1/S

E)

−5 −4 −3 −2 −1 0 1 2 3 4 5estimate of the elasticity of intertemporal substitution

(b) Median estimates reported in studies

020

4060

80pr

ecis

ion

of th

e es

timat

e (1

/SE

)

−1 0 1 2 3 4estimate of the elasticity of intertemporal substitution

Notes: In the absence of selective reporting the funnel should be symmetrical around the most precise estimates.

I exclude estimates with extreme magnitude or precision from the figure but include all in the regressions.

Panel (a) of Figure 1 shows the funnel plot with all estimates of the EIS. The most precise

estimates are positive but small. Researchers report negative estimates less often than positive

estimates with the same precision, which makes the arithmetic average of the reported estimates

much larger than the precision-weighted average. It is easier to see the pattern of selective

reporting in panel (b) of Figure 1, where I show only the median estimates reported in the

studies. In fact, equation (2) estimated in Table 1 can be interpreted as a test of the funnel’s

asymmetry. The weighted least squares version of equation (2) follows from rotating the axes of

the funnel plot and dividing the values on the new vertical axis by the standard error to remove

heteroskedasticity.

Figure 2 shows the consequences of the second source of selective reporting: selection of

estimates for statistical significance. The figure depicts the distribution of the median t-statistics

of the estimates reported in the studies. I use median values here because some studies report

many estimates with similar t-statistics, which would distort the histogram. (A histogram using

all estimates is available in the online appendix, where I also report some statistical tests.) From

panel (a) we can see that estimates marginally insignificant at the 5% level are reported less often

than they should be. Panel (b) offers a closer look at the distribution of the t-statistics around

two. When the t-statistics reach the critical value corresponding to statistical significance at

the 10%, 5%, and 1% level, estimates seem to be reported more frequently. The frequency

9

Figure 2: Marginally insignificant estimates are underreported

(a) Histogram of median t-statistics

0.1

.2.3

dens

ity

−2 −1.5 −1 −.5 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5median t−statistic of EIS reported in a study

(b) Median t-statistics around t = 2

0.5

11.

5de

nsity

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8median t−statistic of EIS reported in a study

Notes: In the absence of selective reporting the distribution of the t-statistics should be approximately normal.

The dashed lines in panel (b) denote critical values most often used for determining significance. I exclude

estimates with large t-statistics from the figure but include all in the regressions.

of reported elasticities more than doubles when a conventional critical value is reached, and

decreases sharply just before the t-statistic reaches the next critical value. Together with the

regression results reported in Table 1, Figure 2 presents strong evidence that researchers prefer

to report statistically significant estimates of the EIS.

Hedges (1992) introduces a model of the second source of selective reporting. He assumes

that the probability of reporting of an estimate is determined by its statistical significance and

only changes when the t-statistic reaches a psychological barrier. I prefer the funnel asymmetry

test, because it is more flexible and captures both sources of selective reporting. Nevertheless,

I estimate Hedges’ model and report the results in the online appendix. The results of Hedges’

model also suggest substantial selective reporting in the literature.

4 Method Choices

So far I have assumed that all differences in the estimates are due to sampling error and selective

reporting. But in reality the estimates come from studies that use various data sets and methods,

which may themselves lead to systematically different results. To explain the differences in the

results I collect 30 variables reflecting the utility function used in the study, characteristics of the

data, design of the analysis, definition of variables, estimation characteristics, and publication

10

characteristics. I add these variables, described in Table A2 in the Appendix, to regression (2),

which yields

EISij = EIS0 + β · SE(EISij) + γXij + vij , (3)

where X is a vector of the 30 characteristics of the estimates. The constant in the regression

still denotes the underlying EIS corrected for reporting bias, but now the constant must be

interpreted together with X. In this specification the constant represents the underlying EIS

conditional on X = 0. The following paragraphs describe why different method choices could

influence the reported elasticities.

Utility function I create a dummy variable that equals one if the researcher assumes Epstein-

Zin preferences and separates the EIS from the coefficient of relative risk aversion. Some studies

assume Epstein-Zin preferences but use a log-linear approximation of the Euler equation, which

leads to the same estimation model as with time-separable utility; for these estimates I set

the dummy variable to zero. With time-separable utility the curvature of the utility kernel

carries information about both risk aversion and intertemporal substitution. Hall (1988) argues

that the interpretation of the estimated parameter as describing intertemporal substitution is

natural, while Kocherlakota (1990) suggests that the parameter captures risk aversion and says

little about intertemporal substitution. If risk aversion drives the estimate of the curvature

parameter, our inference concerning the EIS estimated within the framework of time-separable

utility will be biased. The direction of the bias depends on whether the true EIS is smaller or

larger than the inverse of the coefficient of relative risk aversion.

Some authors assume habits in consumption; in their estimations they usually include lagged

values of consumption in the log-linearized Euler equation (as in Dynan, 2000). If habit forma-

tion is significant, the estimated coefficients on the rate of return will be systematically smaller

than the coefficients obtained without habit formation. Dynan (2000), however, finds little

evidence for habit formation and even reports a negative coefficient for lagged consumption,

which contributes to larger estimates of the coefficient on the rate of return.

Ogaki & Reinhart (1998) show that assuming separability between durable and nondurable

consumption goods can produce a downward bias in the estimates of the EIS. An increase in

the interest rate increases this year’s user cost for the service flow from purchasing durable

11

goods, so the consumer substitutes away to nondurables. If the change in the user cost is not

compensated next year, the growth rate of the consumption of nondurables decreases, leading

to smaller estimates of the EIS. Authors allowing for nonseparability between durables and

nondurables use cointegration estimation methods.

Amano & Wirjanto (1997) find that intratemporal substitution between private and public

consumption is important, so that the typical assumption of separability between these two

types of consumption is restrictive. They also argue that their cointegration technique is more

flexible than the usual GMM approach, as it does not require the assumption of, for example, the

absence of liquidity constraints and constant preference shocks. Amano & Wirjanto (1997) note

that their method produces smaller estimates of the EIS compared to GMM. Similarly, Ostry

& Reinhart (1992) argue that it is important to distinguish between tradable and nontradable

consumption goods. They report larger estimates of the EIS than what is typically found in

the literature.

Data characteristics I include the logarithm of the number of cross-sectional units (house-

holds, cohorts, or countries) used in the estimation of the EIS to see whether the breadth of

the data has an influence on the results. It is natural to put more confidence in large studies,

which should display little small-sample bias. In a similar vein I control for the number of years

of the data used in the estimation, because Attanasio & Low (2004) show that log-linearized

Euler equations only give consistent estimates when the available time span of the data is long.

I also allow the EIS to vary in time by controlling for the average year of the data period used in

the estimation. Perhaps financial innovations lessen the constraints that hinder intertemporal

substitution; changes in disposable income and stock market participation can also affect the

estimated elasticity.

Attanasio & Weber (1993) note that estimating Euler equations on macro data can lead to

a downward bias in the estimated EIS because of, for example, the omission of demographic

factors. A growing proportion of studies have used micro data to estimate the elasticity, and I

control for this aspect of methodology to see what the systematic effect of micro estimation is

on the reported elasticity.

Bansal et al. (2012) stress the difference between consumers’ decision frequency and the

econometrician’s sampling frequency of the data. They estimate the decision frequency to be

12

approximately monthly and show that estimating the EIS with a lower sampling frequency

without taking into account temporal aggregation leads to a substantial downward bias. I

include dummy variables for annual and monthly sampling frequencies used to estimate the

EIS, with the most common quarterly frequency as the base.

Design of the analysis I distinguish between two groups of micro studies estimating the

EIS. The first, larger group uses household-level data on consumption, usually from the Panel

Study of Income Dynamics. The second group constructs panels of birth cohorts to estimate

the elasticity (for example, Blundell et al., 1994; Attanasio & Browning, 1995). Gruber (2006)

notes that in the latter group of studies the identification of the elasticity comes from time

series variation correlated with consumption, which may lead to a downward bias. Similarly,

according to Lawrance (1991), the first group of micro studies should include time dummies for

the identification to come from cross-sectional variation.

There is little consensus in the literature on the natural normalization of consumers’ first-

order condition for optimal portfolio choice. Some authors follow Hall (1988), regress con-

sumption growth on the rate of return, and interpret the resulting coefficient as the EIS. Others

follow the normalization of Hansen & Singleton (1982), regress the rate of return on consumption

growth, and interpret the resulting coefficient as the inverse of the EIS (or, with time-separable

utility, the coefficient of relative risk aversion). Both practices are asymptotically equivalent,

but Yogo (2004) shows that they lead to different results due to the small-sample bias stemming

from the use of weak instruments. In practice, the choice of normalization depends on whether

consumption growth or the rate of return is more difficult to predict. Campbell (1999) argues

that the normalization of Hall (1988) may help with the weak instrument problem because good

instruments for consumption growth are harder to find. Beeler & Campbell (2012) note that

since a large EIS is consistent with more predictable consumption growth, the normalization of

Hansen & Singleton (1982) is more suitable when the underlying EIS is large, while when the

EIS is small the normalization of Hall (1988) is preferred.

Some studies estimate the EIS separately for rich households or asset holders. Poor con-

sumers may substitute less intertemporally because their consumption bundle contains a larger

share of necessities, which are more difficult to substitute between time periods. Evidence for

a larger EIS among the rich is reported by Attanasio & Browning (1995) using micro data

13

and Ogaki et al. (1996) using cross-country data. Exposure to the stock market may also be

correlated with households’ awareness of the benefits of intertemporal substitution; Mankiw &

Zeldes (1991) find a larger EIS for stockholders than for nonstockholders. I include a dummy

that equals one if the estimate is related to the rich or asset holders.

Hall (1988) illustrates why first lags of variables should not be used as instruments because of

the time aggregation of consumption. He argues that time aggregation makes the instruments

used by Hansen & Singleton (1982) correlated with the error terms in the estimated Euler

equation, which may explain why Hansen & Singleton (1982) and other studies following their

approach find much larger estimates of the EIS compared with Hall (1988).

A number of studies focus on excess sensitivity of consumption to current income; in most

cases they include a measure of income in the log-linearized Euler equation using the normal-

ization of Hall (1988). If there is some excess sensitivity, the estimated regression coefficient

on the rate of return should be smaller than in the case of no excess sensitivity, so I expect a

negative sign for the regression coefficient of the dummy variable corresponding to this aspect

of methodology. Moreover, I acccount for the number of controls for taste shifters (such as age,

family size, education, and marital status) used in micro studies estimating the EIS.

Variable definition Most studies use nondurable consumption as a proxy for total consump-

tion; durable goods are usually excluded because of the volatility of spending on durables and

the problems with imputing a service flow to the stock of durables. I create a dummy vari-

able that equals one for studies that include durables in the consumption proxy. For example,

Mankiw (1985) estimates a larger EIS for the consumption of durable goods than for non-

durable consumption. Some studies use food expenditure as the consumption proxy, a practice

criticized by Attanasio & Weber (1995) on the grounds of nonseparability between food and

other consumption. Food is a necessity, and intertemporal substitution of other components of

consumption is probably easier, which leads to a downward bias in the EIS when researchers

rely on food as a proxy for consumption.

The typical proxy for the rate of return used in the consumption Euler equation is the return

on treasury bills. Some studies use stock returns, but these are more difficult to predict, which

magnifies the weak instrument problem and may lead to a downward bias in the estimated

EIS, as mentioned by Vissing-Jorgensen (2002). Mulligan (2002) argues that the rate of return

14

should be measured as the expected return on a representative unit of capital. Few researchers

follow his approach, but I include a dummy that equals one if the researcher uses more than

one measure of the rate of return to estimate the EIS.

Estimation characteristics I distinguish between studies that estimate the exact Euler

equation and studies that use log-linear approximation. Carroll (2001) is skeptical about the

use of log-linearized consumption Euler equations for the estimation of the EIS, because higher-

order terms may be endogenous to omitted variables. In contrast, Attanasio & Low (2004)

argue that the log-linear Euler equation performs better than non-linear GMM.

Most studies use GMM to estimate the Euler equation. Sometimes TSLS is used, which,

in contrast to GMM, requires the assumption of homoskedastic error. A few researchers use

methods based on maximum likelihood, especially limited information maximum likelihood.

Yogo (2004) notes that the latter technique could be more reliable in the case of weak instru-

ments. Several authors assume away the simultaneity problem and use OLS to estimate the

log-linearized Euler equation. Neely et al. (2001) suggest that, because the weak instrument

problem is so difficult to overcome, this simplification can lead to more stable and sensible

estimates of the EIS.

Publication characteristics While I try to control for as many aspects of methodology

as possible, some important advances in methodology cannot be examined in this framework

because they have been employed by only a few studies—the corresponding dummy variable in

my analysis would have little variation. For example, Bansal & Yaron (2004) argue that time-

varying consumption volatility should be taken into account, as ignoring it leads to a downward

bias in the estimates of the EIS. (On the other hand, Beeler & Campbell, 2012, question the

extent of the bias.) To see whether new methods not captured by the variables explained above

have a systematic influence on the estimated EIS, I include the study publication year in the

analysis. As an additional control for study quality I include the logarithm of the number of

Google Scholar citations per year, the recursive RePEc impact factor of the journal, and a

dummy variable that equals one for studies published in the top five general interest journals.

My intention is to find out what aspects of methodology have a systematic influence on the

estimated EIS and whether the estimated coefficient for reporting bias survives the addition of

15

variables reflecting heterogeneity. Moreover, I would like to estimate the corrected EIS reported

in micro studies, and especially for asset holders, while controlling for method characteristics.

Vissing-Jorgensen (2002) argues that the EIS of asset holders represents the underlying elasticity

better than does the mean over all households. Guvenen (2006) shows that the dilemma between

the large EIS required by most macro models and small empirical estimates can arise when the

elasticity differs across groups of people: the rich (or asset holders) have a higher EIS than the

rest of the population. The EIS of the asset holders determines fluctuations in investment and

output, which makes the estimate more suitable for calibration—at least if the model focuses

on inference concerning aggregates linked to wealth.

Table 2 presents the results of regression (3). Some method variables have the same value

for all estimates reported in a study, so I do not use fixed effects as I need both between and

within-study variation. I use sampling weights equal to the inverse of the number of estimates

reported in a study to take into account that some studies report many more estimates than

others. The first column of the table includes only dummy variables for micro data and asset

holders additionally to the standard error. As expected, micro studies and studies focusing on

the rich and asset holders report substantially larger elasticities. The estimation yields a large

coefficient for reporting bias (2.5) and a negligible EIS beyond the bias for macro studies (the

constant at the bottom of the table; 0.02), which is consistent with the results reported in the

last section. The corrected elasticity for micro studies is 0.22, and for micro estimates related to

asset holders the elasticity reaches 0.36 (= 0.0237+0.200+0.136) with a narrow 95% confidence

interval [0.33, 0.39].

In the next columns of Table 2 I add groups of variables reflecting different aspects of the

studies and estimates discussed in the paragraphs above. The estimated magnitude of the

reporting bias decreases from 2.5, but oscillates around two in all specifications and retains

statistical significance at the 1% level. The difference between micro and macro studies and

between estimates for asset holders and average consumers increases with the addition of more

variables reflecting method choices. Some of the method choices seem to systematically influence

the reported elasticities.

16

Table 2: Explaining the differences in the reported estimates of the EIS

(1) (2) (3) (4) (5) (6) (7)

SE 2.465∗∗∗

1.926∗∗∗

1.864∗∗∗

2.109∗∗∗

1.975∗∗∗

1.961∗∗∗

1.809∗∗∗

(0.394) (0.251) (0.243) (0.268) (0.261) (0.262) (0.248)

Micro data 0.200∗∗∗

0.209∗∗∗

0.269∗∗∗

0.350∗∗∗

0.476∗∗∗

0.502∗∗∗

0.430∗∗∗

(0.0250) (0.0308) (0.0495) (0.0986) (0.0854) (0.0865) (0.106)

Asset holders 0.136∗∗∗

0.174∗∗∗

0.195∗∗∗

0.189∗∗∗

0.228∗∗∗

0.236∗∗∗

0.316∗∗∗

(0.0303) (0.0365) (0.0626) (0.0565) (0.0482) (0.0460) (0.0586)

Utility

Epstein-Zin -0.0200∗∗∗

-0.0261∗∗∗

-0.0207∗∗∗

-0.0257∗∗∗

-0.0245∗∗∗

-0.0754∗

(0.00655) (0.00699) (0.00738) (0.00742) (0.00623) (0.0384)

Habits 0.425∗∗∗

0.398∗∗∗

0.409∗∗∗

0.292∗∗∗

0.328∗∗∗

0.304∗∗∗

(0.0671) (0.0710) (0.0362) (0.0487) (0.0443) (0.0472)

Nonsep. durables 0.0320∗∗∗

0.0123 0.0309∗

0.0261∗

0.0265 0.0367∗

(0.00324) (0.0122) (0.0163) (0.0156) (0.0160) (0.0190)Nonsep. public 0.0709 0.109 0.117 0.0399 0.0560 0.0959

(0.0871) (0.0952) (0.0916) (0.0964) (0.0881) (0.0921)

Nonsep. tradables 0.358∗∗∗

0.328∗∗∗

0.316∗∗∗

0.187∗∗∗

0.195∗∗∗

0.212∗∗∗

(0.0456) (0.0512) (0.0644) (0.0593) (0.0679) (0.0668)

Data

No. of households -0.0114 -0.0254 -0.0447∗∗∗

-0.0504∗∗∗

-0.0595∗∗∗

(0.0101) (0.0163) (0.0142) (0.0138) (0.0171)No. of years 0.00729 0.00317 0.000970 0.000292 -0.00926

(0.00822) (0.00639) (0.00528) (0.00477) (0.0114)

Average year 3.626 4.955∗

3.470 4.286 6.391∗

(2.823) (2.895) (2.430) (2.958) (3.568)Annual data -0.0260 -0.0149 -0.0207 -0.0237 -0.0142

(0.0195) (0.0149) (0.0143) (0.0149) (0.0174)Monthly data -0.00511 -0.0251 0.00324 -0.0284 -0.0368

(0.0107) (0.0224) (0.0188) (0.0521) (0.0538)

Design

Quasipanel -0.0932∗

-0.165∗∗∗

-0.123∗∗∗

-0.0886∗

(0.0554) (0.0442) (0.0403) (0.0490)

Inverse estimation 0.0392 0.0397 0.0513∗

0.0225(0.0240) (0.0275) (0.0294) (0.0429)

First lag instrument -0.00893 0.0133 0.0111 0.0415(0.0218) (0.0204) (0.0307) (0.0274)

No year dummies -0.458∗∗∗

-0.237 -0.240 -0.222(0.161) (0.219) (0.210) (0.218)

Income -0.0218 -0.0315∗∗

-0.0328 -0.0350(0.0172) (0.0127) (0.0201) (0.0230)

Taste shifters 0.0649∗∗

0.0423∗∗

0.0375∗

0.0712∗∗

(0.0251) (0.0203) (0.0207) (0.0310)

Variable definition

Total consumption 0.102∗∗∗

0.114∗∗∗

0.0888∗∗∗

(0.0242) (0.0292) (0.0337)Food -0.120 -0.0827 -0.0689

(0.187) (0.181) (0.193)Stock return -0.00760 -0.00659 -0.00444

(0.0126) (0.0112) (0.00960)Capital return -0.0431 -0.0476 -0.0472

(0.0327) (0.0385) (0.0411)

EstimationExact Euler 0.0606 0.0477

Continued on the next page

17

Table 2: Explaining the differences in the reported estimates of the EIS (continued)

(1) (2) (3) (4) (5) (6) (7)

(0.0384) (0.0345)ML 0.0874 0.130

(0.0770) (0.0830)TSLS 0.0641 0.0284

(0.0459) (0.0553)OLS 0.102 0.0887

(0.0665) (0.0710)

PublicationPublication year -0.609

(6.062)

Citations 0.0255∗

(0.0150)Top journal 0.0945

(0.0765)Impact -0.0185

(0.0272)

Constant 0.0237∗∗

0.00512 -27.52 -37.61∗

-26.33 -32.58 -43.89(0.0109) (0.00322) (21.42) (21.97) (18.44) (22.45) (43.05)

Observations 2,735 2,735 2,735 2,735 2,735 2,735 2,735Studies 169 169 169 169 169 169 169

Notes: The table presents the results of regression EISij = EIS0+β ·SE(EISij)+γXij+uij . EISij and SE(EISij) arethe i-th estimates of the elasticity of intertemporal substitution and their standard errors reported in the j-th studies.X is a vector of the estimates’ characteristics described in Table A2. Estimated with sampling weights equal to theinverse of the number of estimates reported in the j-th studies. Standard errors are robust, clustered at the study level,and shown in parentheses.

∗∗∗,

∗∗, and

∗denote statistical significance at the 1%, 5%, and 10% level.

Utility function When researchers assume Epstein-Zin utility and disentangle the EIS from

the coefficient of relative risk aversion, they tend to find systematically smaller estimates of the

elasticity, but only by 0.02–0.03 on average. Therefore, my results do not show a substantial

bias in the estimated EIS due to the use of time-separable utility. In contrast, when habits in

consumption are assumed, the reported EIS are likely to be much larger than without habits:

by 0.3–0.4. I have noted that the reported coefficients should decrease as the strength of

habit formation increases, so the result probably reflects the fact that many studies find an

insignificant (or even negative) coefficient on lagged consumption; for example, Dynan (2000).

Moreover, only a few studies that estimate the EIS assume habits.

Not allowing for nonseparability between durables and nondurables creates a downward bias

in the estimates of the EIS, consistent with the argument of Ogaki & Reinhart (1998), but the

bias is only 0.02–0.03 and the regression coefficient corresponding to this dummy variable is

statistically insignificant in some specifications. It does not seem to matter for the estimates

of the EIS whether separability between private and public consumption is assumed. On the

18

other hand, not allowing for nonseparability between tradable and nontradable consumption

goods leads to a substantial downward bias of 0.2–0.3, which corroborates the results of Ostry

& Reinhart (1992).

Data characteristics The results suggest that the characteristics of the data, other than

the choice between micro and macro estimation, have little influence on the reported estimates

of the EIS. Larger studies seem to be associated with lower estimates, but the corresponding

regression coefficient is small and statistically insignificant in some specifications. I do not find

a systematic bias in studies that use short time series to estimate the EIS. Studies using newer

data are associated with somewhat larger reported elasticities, but the effect is not significant

at the 5% level in any specification. Finally, the data sampling frequency matters little for the

estimated EIS once I control for the definition of the utility function.

Design of the analysis Studies that construct panels of birth cohorts to estimate the EIS

tend to report elasticities about 0.1 smaller than studies using household-level consumption

data. In contrast, the choice of the normalization of the Euler equation (that is, whether to

regress consumption growth on the rate of return or the other way round) has little effect on

the reported EIS. Similarly the use of first lags of variables as instruments does not create a

substantial bias. It matters for the micro studies whether or not year fixed effects are included in

the estimation: when the identification comes from tax rate variation and not from time-series

factors, the estimated elasticities tend to be 0.2–0.4 smaller, but the corresponding regression

coefficients have large standard errors. The inclusion of income in the Euler equation does not

affect the reported EIS much. The inclusion of taste shifters, however, is important: studies

that control for more demographic characteristics report larger elasticities.

Variable definition The choice of the proxy for consumption has important consequences

for the estimated elasticity. I find that the inclusion of durable goods in the proxy significantly

increases the EIS (by about 0.1), which is consistent with the results of Mankiw (1985). The

use of food as the proxy for consumption does not lead to a significant bias in the reported EIS.

Finally, the choice of the proxy for the rate of return has no systematic consequences for the

results.

19

Estimation characteristics Different estimation techniques do not produce systematically

different estimates of the elasticity. OLS, GMM, TSLS, and maximum likelihood-based methods

all yield similar results on average when I control for other aspects of methodology. Studies

estimating exact and log-linearized Euler equations also report similar elasticities.

Publication characteristics After I control for all the method choices discussed above, I

also include several publication characteristics. Other things being equal, newer studies do

not generate substantially different estimates of the EIS. This result suggests that my proxies

for method choices capture any systematic differences in the reported EIS that are correlated

with the year of publication. The additional proxies for study quality (the number of citations,

publication in a top journal, and the recursive impact factor of the journal) do not affect the

reported elasticities once I control for method choices.

Now I turn back to estimating the underlying elasticity for asset holders to see what the

effect is of the additional method choices taken together. Because of the many variables in

columns 2–7 it is difficult to discern the underlying elasticity; it depends on the values of all the

additional variables. I take the last column of the table and choose a preferred value for each

variable to get an estimate conditional on “best practice.” I put quotes around best practice

here because the definition is subjective, no study can address all potential problems in the

literature simultaneously, and some of my variables do not capture methodology—for example,

the number of citations or the journal impact factor. We can also imagine the result as an

aggregated EIS with more weight given to the estimates’ characteristics that can be considered

in some way better than others.

My definition of best practice is the following. I prefer if the first lag of variables is not

included among instruments—which is to say I plug in value “0” for the dummy variable First

lag instrument in column 7 of Table 2. I prefer if nondurable consumption, not just food, is

used as the dependent variable; if micro studies include time dummies; if the model allows

for nonseparability between durables and nondurables; if the rate of return is measured as the

return on capital; if the researcher uses micro data; if the researcher does not use the log-linear

approximation of the Euler equation; if the study employs the normalization of Hall (1988);

if the study differentiates between the EIS and the coefficient of relative risk aversion; if the

20

regression is estimated by GMM; and if the study is published in a top journal. I also plug in the

maximum number of cross-sectional units used in my sample of studies, the maximum number

of years of the data period, the maximum average year of the data, the maximum number of

citations of the study, and the maximum impact factor of the outlet. I set all other variables

to their sample means.

The resulting estimate of the EIS for asset holders is a linear combination of regression

parameters conditional on my definition of best practice. I get a point estimate of 0.33, which is

close to the previous estimate unconditional on methodology (0.36). The estimate conditional

on best practice, however, has a much wider 95% confidence interval: [−0.2, 0.8]. This estimate

of the EIS is corrected for both the reporting bias and potential mistakes in measurement. I

would get a different estimate if I chose a different definition of best practice, but in general

the supposed misspecifications taken together do not seem to have a systematic effect on the

estimated EIS. I believe it is safe to say that calibrations of the EIS greater than 0.8 are

inconsistent with the literature estimating the elasticity.

The order in which I add the groups of control variables into Table 2 is arbitrary. I also derive

the best-practice estimate from the last column that includes all variables, even though most of

them are insignificant: the last column is probably not the best possible model for explaining the

heterogeneity in the estimates of the EIS. So, as a robustness check, I employ Bayesian model

averaging to address model uncertainty. Bayesian model averaging runs many regressions that

include the possible subsets of all explanatory variables and constructs a weighted average over

these regressions. (The weights are roughly proportional to the goodness of fit of the different

regressions.) The results of Bayesian model averaging, available in the online appendix, are

consistent with those reported here.

I have noted, based on the results reported in Table 2, that the inclusion of controls for es-

timate and study characteristics does not alter the relationship identified between the reported

estimates of the EIS and their standard errors—the selective reporting bias. But even though I

include 30 control variables, I cannot hope to capture all methodological differences among the

estimates. If I fail to control for a method choice that affects the estimates and standard errors

in the same direction (and if at the same time the effect is not offset by omitted method choices

that have an opposite influence on the estimates and standard errors), my results concerning

21

the relationship between the two variables will be exaggerated. In extreme cases the relation-

ship may be entirely due to unobserved differences in methodology that jointly determine the

estimates and standard errors.

To test whether unobserved differences in methodology affect my results, I exploit the fact

that the standard error of a regression parameter is proportional to the inverse of the square

root of the number of degrees of freedom used in the regression. While I do not have data

on the number of degrees of freedom, I have information on a closely related statistic, the

number of observations. Therefore the inverse of the square root of the number of observations

used by researchers to obtain the EIS represents a natural instrument for the standard error of

the estimate. The first column of Table 3 re-estimates my baseline specification for detecting

selective reporting, the first column of Table 1, but instruments the variable on the right-hand

side. The Kleibergen-Paap test rejects the hypothesis of underidentification at the 5% level.

The estimated regression coefficients are similar to those in the baseline specification, but the

estimates are predictably less precise: the standard errors are about four times larger. Even so,

the coefficient associated with selective reporting is statistically significant at the 5% level.

Table 3: The relation between estimates and standard errors is not driven by method choices

IV Proxy

FE Pooled FE Pooled

SE 2.433∗∗

1.802∗∗∗

1.601∗∗∗

1.718∗∗∗

(0.972) (0.241) (0.314) (0.262)

Constant 0.000840 -8.250 0.0274∗∗∗

0.00242(0.0416) (5.114) (0.0101) (0.00338)

Utility definition Included IncludedData characteristics Included IncludedDesign char. Included IncludedVariable def. Included IncludedEstimation char. Included IncludedPublication char. Included Included

Observations 2,735 2,735 2,735 2,735Studies 169 169 169 169

Notes: The table shows modifications of the baseline regression reported in the first column of Table 1:EISij = EIS0 + β · SE(EISij) + uij , where EISij and SE(EISij) are the i-th estimates of the elasticityof intertemporal substitution and their standard errors reported in the j-th studies. IV = the inverse of thesquare root of the number of observations is used as an instrument for the standard error. Proxy = the inverseof the square root of the number of observations is used as a proxy for the standard error. FE = study fixedeffects. Pooled = estimate and study characteristics, described in Table A2, are included; no fixed effects.∗∗∗

and∗∗

denote statistical significance at the 1% and 5% level. See also notes to Table 1 and Table 2.

22

I believe it is plausible to assume that the number of observations is little correlated with

most method choices, so that it represents a valid instrument. Nevertheless, important data

characteristics such as the difference between micro and macro approaches are correlated with

the number of observations, so in the second column of Table 3 I take these characteristics out of

the error term. The second column of Table 3 therefore re-estimates the last column of Table 2,

but again uses the inverse of the square root of the number of observations as an instrument.

The resulting coefficient for selective reporting is smaller, but still statistically significant and

close to two. I obtain similar results when I use the inverse of the square root of the number

of observations as a proxy instead of an instrument for the standard error (the remaining two

columns of Table 3). I conclude that the relationship between the estimates of the EIS and

their standard errors is not driven by unobserved differences in methodology.

5 Conclusion

Selective reporting creates a bias of about 1/2 in the mean published estimate of the elasticity

of intertemporal substitution, which is more than the effect of any method choice. Only the

choices between micro and macro data and between asset holders and all households create

differences in the estimated EIS of a similar magnitude to the effects of selective reporting.

Corrected for the reporting bias, the micro estimates for asset holders are around 1/3, and the

number does not change much when I estimate the EIS conditional on many method choices to

correct for the supposed mistakes in measurement discussed in the literature.

My results suggest that the published literature estimating the EIS is consistent with the

elasticity lying deep below 1, which is in line with Hall (1988) and Campbell (2003), and,

among other things, implies that agents’ optimal consumption-wealth ratio increases in expected

returns (Campbell & Viceira, 1999). Macroeconomic models typically require an EIS close to 1,

but Braun & Nakajima (2012) show how a small EIS can be compatible with macroeconomic

facts. The major caveat of my results is the impossibility to examine the effects of some recent

advances in methodology that have been employed by only a few studies: for example, taking

into account stochastic volatility in consumption based on Bansal & Yaron (2004). Nevertheless,

the reported estimates do not increase with the year of publication, which suggests that newer

methods do not yield substantially larger estimates.

23

References

Ai, H. (2010): “Information Quality and Long-Run Risk: Asset Pricing Implications.” Journal of Finance 65(4):pp. 1333–1367.

Amano, R. A. & T. S. Wirjanto (1997): “Intratemporal Substitution And Government Spending.” The Reviewof Economics and Statistics 79(4): pp. 605–609.

Ashenfelter, O. & M. Greenstone (2004): “Estimating the Value of a Statistical Life: The Importance ofOmitted Variables and Publication Bias.” American Economic Review 94(2): pp. 454–460.

Attanasio, O. P. & M. Browning (1995): “Consumption over the Life Cycle and over the Business Cycle.”American Economic Review 85(5): pp. 1118–37.

Attanasio, O. P. & H. Low (2004): “Estimating Euler Equations.” Review of Economic Dynamics 7(2): pp.405–435.

Attanasio, O. P. & G. Weber (1989): “Intertemporal Substitution, Risk Aversion and the Euler Equation forConsumption.” Economic Journal 99(395): pp. 59–73.

Attanasio, O. P. & G. Weber (1993): “Consumption Growth, the Interest Rate and Aggregation.” Review ofEconomic Studies 60(3): pp. 631–49.

Attanasio, O. P. & G. Weber (1995): “Is Consumption Growth Consistent with Intertemporal Optimization?Evidence from the Consumer Expenditure Survey.” Journal of Political Economy 103(6): pp. 1121–57.

Bansal, R., D. Kiku, & A. Yaron (2007): “Risks for the Long Run: Estimation and Inference.” Working paper,Duke University and University of Pennsylvania.

Bansal, R., D. Kiku, & A. Yaron (2012): “Risks For the Long Run: Estimation with Time Aggregation.”NBER Working Papers 18305, National Bureau of Economic Research, Inc.

Bansal, R. & A. Yaron (2004): “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.”Journal of Finance 59(4): pp. 1481–1509.

Barro, R. J. (2009): “Rare Disasters, Asset Prices, and Welfare Costs.” American Economic Review 99(1):pp. 243–64.

Barsky, R. B., M. S. Kimball, F. T. Juster, & M. D. Shapiro (1997): “Preference Parameters and BehavioralHeterogeneity: An Experimental Approach in the Health and Retirement Study.” The Quarterly Journal ofEconomics 112(2): pp. 537–79.

Beeler, J. & J. Y. Campbell (2012): “The Long-Run Risks Model and Aggregate Asset Prices: An EmpiricalAssessment.” Critical Finance Review 1(1): pp. 141–182.

Blundell, R., M. Browning, & C. Meghir (1994): “Consumer Demand and the Life-Cycle Allocation ofHousehold Expenditures.” Review of Economic Studies 61(1): pp. 57–80.

Braun, R. A. & T. Nakajima (2012): “Making the Case for a Low Intertemporal Elasticity of Substitution.”Working Paper 2012-01, Federal Reserve Bank of Atlanta.

Browning, M., L. P. Hansen, & J. J. Heckman (1999): “Micro Data and General Equilibrium Models.”In J. B. Taylor & M. Woodford (editors), “Handbook of Macroeconomics,” volume 1 of Handbook ofMacroeconomics, chapter 8, pp. 543–633. Elsevier.

Browning, M. & A. Lusardi (1996): “Household Saving: Micro Theories and Micro Facts.” Journal of EconomicLiterature 34(4): pp. 1797–1855.

Campbell, J. Y. (1999): “Asset Prices, Consumption, and the Business Cycle.” In J. B. Taylor & M. Wood-ford (editors), “Handbook of Macroeconomics,” volume 1 of Handbook of Macroeconomics, chapter 19, pp.1231–1303. Elsevier.

Campbell, J. Y. (2003): “Consumption-based asset pricing.” In G. Constantinides, M. Harris, & R. M.Stulz (editors), “Handbook of the Economics of Finance,” volume 1 of Handbook of the Economics of Finance,chapter 13, pp. 803–887. Elsevier.

Campbell, J. Y. & N. G. Mankiw (1989): “Consumption, Income and Interest Rates: Reinterpreting theTime Series Evidence.” In “NBER Macroeconomics Annual 1989, Volume 4,” NBER Chapters, pp. 185–246.National Bureau of Economic Research, Inc.

Campbell, J. Y. & L. M. Viceira (1999): “Consumption And Portfolio Decisions When Expected Returns AreTime Varying.” The Quarterly Journal of Economics 114(2): pp. 433–495.

Card, D. & A. B. Krueger (1995): “Time-Series Minimum-Wage Studies: A Meta-Analysis.” AmericanEconomic Review 85(2): pp. 238–43.

24

Carroll, C. D. (2001): “Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health tothe Second-Order Approximation).” Advances in Macroeconomics 1: p. 6.

Chari, V. V., P. J. Kehoe, & E. R. McGrattan (2002): “Can Sticky Price Models Generate Volatile andPersistent Real Exchange Rates?” Review of Economic Studies 69(3): pp. 533–63.

Colacito, R. & M. M. Croce (2011): “Risks for the Long Run and the Real Exchange Rate.” Journal ofPolitical Economy 119(1): pp. 153–181.

DeLong, J. B. & K. Lang (1992): “Are All Economic Hypotheses False?” Journal of Political Economy 100(6):pp. 1257–72.

Doucouliagos, H. & T. D. Stanley (2013): “Are All Economic Facts Greatly Exaggerated? Theory Compe-tition and Selectivity.” Journal of Economic Surveys 27(2): pp. 316–339.

Dynan, K. E. (2000): “Habit Formation in Consumer Preferences: Evidence from Panel Data.” AmericanEconomic Review 90(3): pp. 391–406.

Egger, M., G. D. Smith, M. Scheider, & C. Minder (1997): “Bias in Meta-Analysis Detected by a Simple,Graphical Test.” British Medical Journal 316: pp. 629–634.

Gorg, H. & E. Strobl (2001): “Multinational Companies and Productivity Spillovers: A Meta-analysis.” TheEconomic Journal 111(475): pp. F723–39.

Gruber, J. (2006): “A Tax-Based Estimate of the Elasticity of Intertemporal Substitution.” NBER WorkingPapers 11945, National Bureau of Economic Research, Inc.

Guvenen, F. (2006): “Reconciling Conflicting Evidence on the Elasticity of Intertemporal Substitution: AMacroeconomic Perspective.” Journal of Monetary Economics 53(7): pp. 1451–1472.

Hall, R. E. (1988): “Intertemporal Substitution in Consumption.” Journal of Political Economy 96(2): pp.339–57.

Hansen, L. P. & K. J. Singleton (1982): “Generalized Instrumental Variables Estimation of Nonlinear RationalExpectations Models.” Econometrica 50(5): pp. 1269–86.

Havranek, T., R. Horvath, Z. Irsova, & M. Rusnak (2013): “Cross-Country Heterogeneity in IntertemporalSubstitution.” William Davidson Institute Working Paper 1056, University of Michigan.

Hedges, L. V. (1992): “Modeling Publication Selection Effects in Meta-Analysis.” Statistical Science 7(2): pp.246–255.

House, C. L. & M. D. Shapiro (2006): “Phased-In Tax Cuts and Economic Activity.” American EconomicReview 96(5): pp. 1835–1849.

Jeanne, O. & R. Ranciere (2011): “The Optimal Level of International Reserves For Emerging Market Coun-tries: A New Formula and Some Applications.” Economic Journal 121(555): pp. 905–930.

Jin, K. (2012): “Industrial Structure and Capital Flows.” American Economic Review 102(5): pp. 2111–46.

Kocherlakota, N. R. (1990): “ Disentangling the Coefficient of Relative Risk Aversion from the Elasticity ofIntertemporal Substitution: An Irrelevance Result.” Journal of Finance 45(1): pp. 175–90.

Lawrance, E. C. (1991): “Poverty and the Rate of Time Preference: Evidence from Panel Data.” Journal ofPolitical Economy 99(1): pp. 54–77.

Mankiw, N. G. (1985): “Consumer Durables and the Real Interest Rate.” The Review of Economics andStatistics 67(3): pp. 353–62.

Mankiw, N. G. & S. P. Zeldes (1991): “The Consumption of Stockholders and Non-Stockholders.” NBERWorking Papers 3402, National Bureau of Economic Research, Inc.

Mulligan, C. B. (2002): “Capital, Interest, and Aggregate Intertemporal Substitution.” NBER Working Papers9373, National Bureau of Economic Research, Inc.

Neely, C. J., A. Roy, & C. H. Whiteman (2001): “Risk Aversion versus Intertemporal Substitution: A CaseStudy of Identification Failure in the Intertemporal Consumption Capital Asset Pricing Model.” Journal ofBusiness & Economic Statistics 19(4): pp. 395–403.

Ogaki, M., J. D. Ostry, & C. M. Reinhart (1996): “Saving Behavior in Low- and Middle-Income DevelopingCountries: A Comparison.” IMF Staff Papers 43(1): pp. 38–71.

Ogaki, M. & C. M. Reinhart (1998): “Measuring Intertemporal Substitution: The Role of Durable Goods.”Journal of Political Economy 106(5): pp. 1078–1098.

Ostry, J. & C. Reinhart (1992): “Saving and Terms of Trade Shocks: Evidence from Developing Countries.”

25

MPRA Paper 6976, University Library of Munich, Germany.

Piazzesi, M., M. Schneider, & S. Tuzel (2007): “Housing, Consumption and Asset Pricing.” Journal ofFinancial Economics 83(3): pp. 531–569.

Rudebusch, G. D. & E. T. Swanson (2012): “The Bond Premium in a DSGE Model with Long-Run Real andNominal Risks.” American Economic Journal: Macroeconomics 4(1): pp. 105–43.

Runkle, D. E. (1991): “Liquidity Constraints and the Permanent-Income Hypothesis: Evidence from PanelData.” Journal of Monetary Economics 27(1): pp. 73–98.

Rusnak, M., T. Havranek, & R. Horvath (2013): “How to Solve the Price Puzzle? A Meta-Analysis.” Journalof Money, Credit and Banking 45(1): pp. 37–70.

Siegfried, J. J. (2012): “Minutes of the Meeting of the Executive Committee: Chicago, IL, January 5, 2012.”American Economic Review 102(3): pp. 645–52.

Smets, F. & R. Wouters (2007): “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach.”American Economic Review 97(3): pp. 586–606.

Stanley, T. D. (2001): “Wheat from Chaff: Meta-Analysis as Quantitative Literature Review.” Journal ofEconomic Perspectives 15(3): pp. 131–150.

Stanley, T. D. (2005): “Beyond Publication Bias.” Journal of Economic Surveys 19(3): pp. 309–345.

Stanley, T. D. (2008): “Meta-Regression Methods for Detecting and Estimating Empirical Effects in the Pres-ence of Publication Selection.” Oxford Bulletin of Economics and Statistics 70(1): pp. 103–127.

Trabandt, M. & H. Uhlig (2011): “The Laffer Curve Revisited.” Journal of Monetary Economics 58(4): pp.305–327.

Vissing-Jorgensen, A. (2002): “Limited Asset Market Participation and the Elasticity of Intertemporal Sub-stitution.” Journal of Political Economy 110(4): pp. 825–853.

Yogo, M. (2004): “Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak.” TheReview of Economics and Statistics 86(3): pp. 797–810.

A Appendix

Table A1: Authors calibrate the elasticity of intertemporal substitution differently

Study EIS Comments on the calibration

House & Shapiro(2006)

0.2 p. 1837: “Most empirical evidence indicates that the elasticity ofintertemporal substitution is substantially less than one (see Hall,1988). Our calibration is roughly the average estimate in Hall (1988),Campbell & Mankiw (1989), and Barsky et al. (1997).”

Piazzesi et al. (2007) 0.2 p. 550: “We follow Hall (1988), who estimates σ [EIS] to be around0.2. Studies based on micro data find values for σ that are some-what higher, but not by much. For example, Runkle (1991) reportsan estimate of 0.45 using micro data on food consumption. Attana-sio & Browning (1995) report estimates using CEX data between[0.48, 0.67].”

Chari et al. (2002) 0.2 p. 546: “The literature has a wide range of estimates for the curvatureparameter σ [the inverse of the EIS]. We set σ to 5 and show laterthat this value is critical for generating the right volatility in the realexchange rate.”

Trabandt & Uhlig(2011)

0.5 p. 311: “For the intertemporal elasticity of substitution, a generalconsensus is followed for it to be close to 0.5.”

Jeanne & Ranciere(2011)

0.5 p. 920: “The benchmark risk aversion [the inverse of the EIS] and itsrange of variation are standard in the growth and real business cycleliterature.”

Continued on the next page

26

Authors calibrate the elasticity of intertemporal substitution differently (continued)

Study EIS Comments on the calibration

Jin (2012) 0.5 p. 2130: “The intertemporal elasticity of substitution is set to thestandard value.”

Rudebusch & Swan-son (2012)

0.5 p. 121: “We set the curvature of household utility with respect toconsumption, ϕ, to 2, implying an intertemporal elasticity of substi-tution in consumption of 0.5, which is consistent with estimates inthe micro literature (e.g., Vissing-Jorgensen, 2002).”

Smets & Wouters(2007)

0.67 p. 593: “These [values for the EIS and other parameters] are all quitestandard calibrations.”

Bansal & Yaron(2004)

1.5 p. 1492: “The magnitude for the EIS that we focus on is 1.5. Hansen& Singleton (1982) and Attanasio & Weber (1989) estimate the EISto be well in excess of 1.5. More recently, Vissing-Jorgensen (2002)and Guvenen (2006) also argue that the EIS is well over 1.”

Ai (2010) 2 p. 1357: “Empirical evidence on the magnitude of the EIS parameteris mixed. While Hansen & Singleton (1982), Attanasio & Weber(1989), and Vissing-Jorgensen (2002) estimate the EIS parameter tobe larger than one, other studies, for example, Hall (1988), Campbell(1999), and Browning et al. (1999), argue that the EIS parameter iswell below one. (. . . ) Bansal et al. (2007) estimate the EIS parameterto be 2.43 with a standard deviation of 1.3.”

Barro (2009) 2 p. 252: “Because of the shortcomings of macroeconomic estimates ofthe EIS, it is worthwhile to consider microeconomic evidence. TheGruber (2006) analysis is particularly attractive because it uses cross-individual differences in after-tax real interest rates that derive fromarguably exogenous differences in tax rates on capital income.”

Colacito & Croce(2011)

2 p. 159: “The intertemporal elasticity of substitution is equal to two,a number consistent with the literature on long-run risks. (. . . ) Hall(1988) and many follow-up studies estimate this number to be belowunity. Guvenen (2006) reproduces capital and consumption fluctu-ations as long as most of the wealth is held by a small fraction ofthe population with a high elasticity of intertemporal substitution.Attanasio & Weber (1989) document an intertemporal elasticity ofsubstitution greater than one in the United Kingdom.”

Notes: The table lists baseline calibrations of the elasticity of intertemporal substitution in selected studies. Manyother authors assume EIS = 1 and use logarithmic utility.

Table A2: Description and summary statistics of explanatory variables

Variable Description Mean Std. dev.

UtilityEpstein-Zin =1 if the estimation differentiates between the EIS and the

coefficient of relative risk aversion.0.053 0.224

Habits =1 if habits in consumption are assumed. 0.040 0.196Nonsep. durables =1 if the model allows for nonseparability between durables

and nondurables.0.041 0.199

Nonsep. public =1 if the model allows for nonseparability between private andpublic consumption.

0.044 0.206

Nonsep. tradables =1 if the model allows for nonseparability between tradablesand nontradables.

0.046 0.210

Data

Continued on next page

27

Table A2: Description and summary statistics of explanatory variables (continued)

Variable Description Mean Std. dev.

No. of households The logarithm of the number of cross-sectional units used inthe estimation (households, cohorts, countries).

1.103 2.384

No. of years The logarithm of the number of years of the data period usedin the estimation.

3.184 0.570

Average year The logarithm of the average year of the data period. 7.590 0.006Micro data =1 if the coefficient comes from a micro-level estimation. 0.187 0.390Annual data =1 if the data frequency is annual. 0.328 0.469Monthly data =1 if the data frequency is monthly. 0.097 0.296

DesignQuasipanel =1 if quasipanel (synthetic cohort) data are used. 0.053 0.224Inverse estimation =1 if the rate of return is the dependent variable in the esti-

mation.0.317 0.465

Asset holders =1 if the estimate is related to the rich or asset holders. 0.054 0.226First lag instrument =1 if the first lags of variables are included among instruments. 0.305 0.460No year dummies =1 if year dummies are omitted in micro studies using the

Panel Study of Income Dynamics.0.030 0.171

Income =1 if income is included in the specification. 0.241 0.428Taste shifters The logarithm of the number of controls for taste shifters. 0.117 0.452

Variable definitionTotal consumption =1 if durable consumption is included in the estimation. 0.203 0.402Food =1 if food is used as a proxy for nondurables. 0.059 0.235Stock return =1 if the rate of return is measured as stock return. 0.189 0.392Capital return =1 if the researcher includes more than one measure of the

rate of return.0.113 0.317

EstimationExact Euler =1 if the exact Euler equation is estimated. 0.238 0.426ML =1 if maximum likelihood methods are used for estimation. 0.049 0.216TSLS =1 if two-stage least squares are used for estimation. 0.338 0.473OLS =1 if ordinary least squares are used for estimation. 0.104 0.306

PublicationSE The reported standard error of the estimate of the EIS. 136.9 3,999Publication year The logarithm of the year of publication of the study. 7.601 0.004Citations The logarithm of the number of per-year citations of the study

in Google Scholar.2.024 1.256

Top journal =1 if the study was published in one of the top five journalsin economics.

0.207 0.405

Impact The recursive RePEc impact factor of the outlet. 1.089 1.535

Notes: Collected from published studies estimating the elasticity of intertemporal substitution. The list of studiesis available in the online appendix at meta-analysis.cz/eis.

28